Astudent is taking an exam with 20 mcq questions, where each question has 4 choices and the student is randomly answering those questions (so p=0.25). use r code to answer the following questions: - calculate the probability of getting 1 questions correct? - calculate the probability of getting at least 5 questions correct? - calculate the probability of getting 15 questions correct? - calculate the probability of passing the exam (passing grade is 60%). - simulate a class of 100 students taking the same exam (where again each student is making random guesses). what is the average of the class (or the average of correct answers per student)? - if we increase the class size to 1000 students, what happens to the average? (keep in mind that the true average of the correct answers for any given number of students is simply p * n or 0.25 * 20 = 5 correct answers).